Question 637476: Jack is married to Jill. their son, junior, asked each of them to reveal their ages. Juniors parents decided to tell him but in the form of a puzzle. Jack told Junior, "If you reverse the digits in my age, you'll get your mothers age."
Jill told her son, "the sum of my age and your dad's age is equal to 11 times the difference in our ages"
"Wait a minuet," said junior, "I cant figure out your ages with just those two clues"
"You're right" said Jack "Remember that I am older than you're mother."
What are the ages of Jack and Jill?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Jack is married to Jill. their son, junior, asked each of them to reveal their ages.
Juniors parents decided to tell him but in the form of a puzzle.
Jack told Junior, "If you reverse the digits in my age, you'll get your mothers age."
:
let a = first digit in Jack's age
let b = the 2nd digit
Then
10a + b = Jack's age
and
10b + a = Jill's age
:
"the sum of my age and your dad's age is equal to 11 times the difference in our ages"
(10a+b)+(10b+a) = 11[(10a+b)-(10b+a)]
11a + 11b = 11[10a+b-10b-a]
11(a + b) = 11(9a-9b)
divide both sides by 11
a + b = 9a - 9b
b + 9b = 9a - a
10b = 8a
Divide both sides by 2
5b = 4a
b =  a
Only single digit integer solution
a = 5, b = 4
therefore
54 is Jack's age
and
45 is Jill's age
:
:
See if that checks out in the statement:
"the sum of my age and your dad's age is equal to 11 times the difference in our ages"
54 + 45 = 11(54-45)
99 = 11(9)
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